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Math Help - 2e^2.1

  1. #1
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    2e^2.1

    2e^2.1

    that's two e to the power of 2.1

    does this equal 16.33 (2dp) ?
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  2. #2
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    Re: 2e^2.1

    Hint: \displaystyle \begin{align*} e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \dots \end{align*}

    Substitute \displaystyle \begin{align*} x = 2.1 \end{align*} and evaluate to as much accuracy as you desire.
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  3. #3
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    Re: 2e^2.1

    Quote Originally Posted by mathsgirl123431 View Post
    2e^2.1

    that's two e to the power of 2.1

    does this equal 16.33 (2dp) ?
    Yes.

    Quote Originally Posted by Prove It View Post
    Hint: \displaystyle \begin{align*} e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \dots \end{align*}

    Substitute \displaystyle \begin{align*} x = 2.1 \end{align*} and evaluate to as much accuracy as you desire.
    To calculate e^{2.1} to 2 decimal places would require computing up to \frac{x^9}{9!}.
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  4. #4
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    Re: 2e^2.1

    Thanks guys, I appreciate the help
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  5. #5
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    Re: 2e^2.1

    If it were me, I would use a calculator!
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  6. #6
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    Re: 2e^2.1

    Here's another perfectly fine way of doing this. You know how to take integer powers and suppose you have e handy, to good precision. What can we do then? We have

    2e^{2.1} = 2e^2 e^{1/10}

    Now you can use the Taylor series for that last exponential

    e^{1/h} = 1+\frac{1}{h}+\frac{1}{2h^2}+\frac{1}{6}h^3 + \cdots

    If you have 2e^2 to several decimal places in precision, then you can get away with using less terms in this series. It's not a big save but it's kind of neat.
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  7. #7
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    Re: 2e^2.1

    Quote Originally Posted by HallsofIvy View Post
    If it were me, I would use a calculator!
    YES!
    Like, why use the arithmetic series formula to add 1+2+3 ?
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  8. #8
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    Re: 2e^2.1

    I have finished up with the following and I want to find t;

    2.6 = (e^-0.2t) + (e^-0.5t)

    Any help and pointers would be appreciated. Thank you
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  9. #9
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    Re: 2e^2.1

    Denote x = e^(-0.1t). Then your equation is 2.6 = x^2 + x^5. This will probably have to be solved numerically.
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